Deep learning in image classification has achieved remarkable success but at the cost of high resource demands. Model compression through automatic joint pruning-quantization addresses this issue, yet most existing techniques overlook a critical aspect: layer correlations. These correlations are essential as they expose redundant computations across layers, and leveraging them facilitates efficient design space exploration. This study employs Graph Neural Networks (GNN) to learn these inter-layer relationships, thereby optimizing the pruning-quantization strategy for the targeted model. This approach has yielded a 99.36% reduction in complexity for ResNet20 on CIFAR-10, with only a minimal 0.11% drop in accuracy. Furthermore, the integration of GNN sped up the convergence process, reducing iterations by 2.46 times on average, compared to methods without GNN.